{
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   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "#matplotlib包可用于作图，且设置成嵌入显示\n",
    "%matplotlib inline\n",
    "import torch\n",
    "from IPython import display\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'torch.Tensor'> torch.Size([1000, 2])\n",
      "<class 'torch.Tensor'> torch.Size([1000])\n"
     ]
    }
   ],
   "source": [
    "# 生成数据集\n",
    "# 构造一个简单的人工训练数据集\n",
    "# 设训练数据集样本数为1000，输入个数（特征数）为2\n",
    "# 真实权重 w=[2,−3.4], 偏差b=4.2,\n",
    "# 利用随机噪声项 ϵ 来生成标签 y=Xw+b+ϵ\n",
    "\n",
    "num_inputs = 2\n",
    "num_examples = 1000\n",
    "true_w = [2, -3.4]\n",
    "true_b = 4.2\n",
    "features = torch.randn(num_examples, num_inputs, dtype=torch.float32)\n",
    "labels = true_w[0] * features[:,0] + true_w[1] * features[:,1] + true_b\n",
    "labels += torch.tensor(np.random.normal(0, 0.01, size=labels.size()), dtype=torch.float32)\n",
    "\n",
    "print(type(features), features.shape)\n",
    "print(type(labels), labels.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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   "source": [
    "# 通过生成的第二个特征features[:, 1]和标签 labels 的散点图\n",
    "# 可以更直观地观察两者间的线性关系。\n",
    "\n",
    "def use_svg_display():\n",
    "    # 用矢量图显示\n",
    "    display.set_matplotlib_formats('svg')\n",
    "\n",
    "def set_figsize(figsize=(3.5, 2.5)):\n",
    "    use_svg_display()\n",
    "    # 设置图的尺寸\n",
    "    plt.rcParams['figure.figsize'] = figsize\n",
    "\n",
    "# 打印矢量图并设置图的尺寸\n",
    "set_figsize()\n",
    "plt.scatter(features[:,1].numpy(), labels.numpy(), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 读取数据\n",
    "# 每次返回batch_size（批量大小）个随机样本的特征和标签。\n",
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    random.shuffle(indices) # 打乱读取顺序\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        j = torch.LongTensor(indices[i : min(i+batch_size,num_examples)]) # 最后一次可能不足一个batch\n",
    "        yield features.index_select(0, j), labels.index_select(0, j)"
   ]
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   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([10, 2])\n",
      "torch.Size([10])\n"
     ]
    }
   ],
   "source": [
    "batch_size = 10\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X.shape)\n",
    "    print(y.shape)\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.], requires_grad=True)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
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   "source": [
    "# 初始化模型参数\n",
    "# 权重初始化成均值为0、标准差为0.01的正态随机数，偏差则初始化成0\n",
    "\n",
    "w = torch.tensor(np.random.normal(0, 0.1, (num_inputs, 1)), dtype=torch.float32)\n",
    "b = torch.zeros(1, dtype=torch.float32)\n",
    "\n",
    "# 开启梯度追踪\n",
    "w.requires_grad_(requires_grad=True)\n",
    "b.requires_grad_(requires_grad=True)\n"
   ]
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  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义模型\n",
    "# 线性回归的矢量计算表达式的实现\n",
    "\n",
    "def linreg(X, w, b):\n",
    "    return torch.mm(X, w) + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义损失函数\n",
    "# 使用平方损失来定义线性回归的损失函数\n",
    "\n",
    "def squared_loss(y_hat, y):\n",
    "    # 注意这里返回的是向量, 另外, pytorch里的MSELoss并没有除以 2\n",
    "    return (y_hat - y.view(y_hat.size()))**2 / 2"
   ]
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   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义优化算法\n",
    "# 小批量随机梯度下降算法 sgd, \n",
    "# 自动求梯度模块计算得来的梯度是一个批量样本的梯度和, 将它除以批量大小来得到平均值\n",
    "\n",
    "def sgd(params, lr, batch_size):\n",
    "    for param in params:\n",
    "        # 注意这里更改param时用的param.data\n",
    "        param.data -= lr * param.grad / batch_size"
   ]
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   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.035740\n",
      "epoch 2, loss 0.000123\n",
      "epoch 3, loss 0.000047\n"
     ]
    }
   ],
   "source": [
    "# 训练模型\n",
    "# 在每次迭代中，我们根据当前读取的小批量数据样本（特征X和标签y），\n",
    "# 通过调用反向函数backward计算小批量随机梯度，并调用优化算法sgd迭代模型参数\n",
    "\n",
    "\n",
    "lr  = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg\n",
    "loss = squared_loss\n",
    "batch_size = 10\n",
    "\n",
    "for epoch in range(num_epochs):  # 训练模型一共需要num_epochs个迭代周期\n",
    "    # 在每一个迭代周期中，会使用训练数据集中所有样本一次\n",
    "    # X和y分别是小批量样本的特征和标签\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        l = loss(net(X, w, b), y).sum()  # l是有关小批量数据的损失和\n",
    "        l.backward()  # 小批量的损失对模型参数求梯度\n",
    "        sgd([w, b], lr, batch_size)  # 使用小批量随机梯度下降更新 w 和 b\n",
    "\n",
    "        # 不要忘了梯度清零\n",
    "        w.grad.data.zero_()\n",
    "        b.grad.data.zero_()\n",
    "    # 每训练完所有样本一次，即经过一个epoch的训练\n",
    "    train_l = loss(net(features, w, b), labels)\n",
    "    print('epoch %d, loss %f' % (epoch + 1, train_l.mean().item()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, -3.4] tensor([[ 1.9996],\n",
      "        [-3.3996]], requires_grad=True)\n",
      "4.2 tensor([4.2002], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "# 训练完成后，可以比较学到的参数和用来生成训练集的真实参数。它们应该很接近才对\n",
    "\n",
    "print(true_w, w)\n",
    "print(true_b, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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